Celtic insist they have "no preferred candidate" as they seek a replacement for departing manager Ronny Deila.
The Scottish champions released a short statement following news of talks with Malky Mackay and Brendan Rodgers.
David Moyes, Roy Keane, Paul Lambert and Neil Lennon have also been strongly linked with the vacancy.
"We will take our time to go through this process thoroughly and in the proper manner," added the statement from the Glasgow club.
Deila delivered two titles, taking Celtic to five-in-a-row, but the Norwegian fell at the semi-final stage in both domestic cups this season and suffered a miserable European campaign.
"The club has been and will be speaking to a number of candidates," adds the statement.
"We will continue this process with the aim of identifying a new manager who we believe will deliver success to the club."